Abstract:
This paper presents direct and inverse theorems concerning the approximation of functions
of several variables with bounded p-fluctuation using Walsh polynomials. These theorems provide
estimates for the best approximation of such functions by polynomials in the norm of the space under
consideration. The paper investigates the properties of the Walsh system, which includes piecewise
constant functions, and builds on earlier work on trigonometric and multiplicative systems. The
results are theoretical and have potential applications in such areas as coding theory, digital signal
processing, pattern recognition, and probability theory.
